Q. 19

# A motorcycle has to move with a constant speed on an over-bridge which is in the form of a circular arc of radius R and has a total length L. Suppose the motorcycle starts from the highest point. (a) What can its maximum velocity be for which the contact with the road is not broken at the highest point? (b) If the motorcycle goes at speed 1/√2 times the maximum found in part (a), where will it lose the contact with the road? (c) What maximum uniform speed can it maintain on the bridge if it does not lose contact anywhere on the bridge?

To make the motor cycle not to fly off, we can increase the velocity till it makes the centrifugal force greater than that of gravity. So, the maximum is when it is equal to the force of gravity.

(b) a distance π R/3 along the bridge from the highest point,

We are observing the system from the motorcycle.

The condition for just flying off will be,

We can write

So,

So, it will lose contact at a distance when it moves with 1/√2 times the maximum

(c)

Here,

So,

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